Browsers and login timeouts and memory management

Another forum I frequent inplements a “timeout” mechanism, where every 30 min or so I’m forced to re-login. Someone is claiming this is necessary, as a logged in presence involves an open connection, and it must be closed because it’ll waste server memory.

Now, I know this is crap, since browsers and Web pages are stateless. However, I’m not up to date on the actual mechanics of Web server memory management enough to accurately refute this claim. Any care to educate me?